Detection and discrimination of gliding tones as a function
of frequency transition and center frequency
John P. Madden and Kevin M. Fire
Department of Communication Sciences and Disorders, University of North Dakota, P.O. Box 8040,
University Station, Grand Forks, North Dakota 58202
~Received 25 March 1996; accepted for publication 5 August 1996!
Two experiments were performed to investigate subjects’ ability to detect and discriminate 50-ms
up-glides in frequency in several different conditions. In the first experiment, the subjects indicated
which of two signals increased more in pitch. The comparison, or standard signal, was a sinusoid
which increased in frequency by either 0, 250, or 500 Hz. Center frequencies were 0.5, 1, 2, 4, and
6 kHz. Discrimination thresholds were obtained in both nonroved and roved conditions. In the roved
condition, the actual center frequencies of the signals were varied randomly over a range equal to
0.1 times the nominal center frequency. The second experiment was the same as the first, except that
the standard signals were swept over a frequency range equal to 0.5, 1, and 2 times the equivalent
rectangular bandwidth ~ERB! of the auditory filter at the nominal center frequency. Discrimination
thresholds expressed as DHz/ERB varied little as a function of center frequency as long as the
frequency transition of the standard was a constant proportion of ERB. In addition, discrimination
thresholds did not vary significantly as a function of the frequency extent of the standard when the
extent was one ERB or less, but doubled when the extent was two ERBs. The relatively small
amount of variation in threshold across center frequency and the pattern of variation across different
standard transitions supports a place mechanism of frequency coding for these signals based on the
detection of changes in the excitation pattern. © 1996 Acoustical Society of America.
PACS numbers: 43.66.Ba, 43.66.Fe @WJ#
INTRODUCTION
Frequency glides have interested psychoacousticians for
various reasons, including their similarity to formant transitions ~Collins, 1984!. A major issue that remains only partially understood is whether place or temporal coding is used
in the perception of these sounds. It is known that both types
of information are available in the responses of auditorynerve fibers to frequency-modulated tones ~see Sinex and
Geisler, 1981 for evidence of temporal coding!. This paper
addresses this issue by measuring glide detection and discrimination thresholds across a range of center frequencies
and comparison signals.
Most researchers who have worked in this area ~e.g.,
Sergeant and Harris, 1962; Pollack, 1968; Tsumura et al.,
1973; Arlinger et al., 1977! have measured glide detection,
the ability to distinguish glides from tones that do not change
in frequency. The general finding is that transition extent at
detection threshold is similar to the difference limen for frequency ~the DLF! and does not change greatly as a function
of signal duration, at least for durations greater than about
500 ms. Thresholds increase greatly above 2 kHz, even when
expressed as a proportion of center frequency. In a more
recent study, however, Dooley and Moore ~1988a! obtained
up-glide detection thresholds that were relatively constant
from 0.25 to 8 kHz when expressed in this manner.
Few researchers have investigated glide discrimination,
the ability to distinguish one glide from another. Tyler et al.
~1983! and Dooley and Moore ~1988a! measured the glide
direction difference limen, as well as the difference limen for
frequency ~DLF!. In both studies, variation in the glide direction difference limen across frequency was very similar to
3754
J. Acoust. Soc. Am. 100 (6), December 1996
that of the DLFs, with D f / f increasing at higher center frequencies. Tyler et al. concluded that the correlation between
the glide difference limen and the DLF supported temporal
coding of gliding tones, since it is generally thought that only
temporal coding can account for DLFs obtained with pulsed
tones ~Moore, 1973!. Attempting to account for their results
using Zwicker’s excitation-pattern model of frequency discrimination ~Zwicker, 1970!, Dooley and Moore found that
the data supported an excitation-pattern model through 2
kHz, but departed from its predictions above that center frequency. They concluded that the data did not fully support
the model, but did not provide strong evidence against it,
either.
Studies of frequency modulation ~FM! detection are also
of interest, because, as Dooley and Moore ~1988a! state, frequency glides ‘‘can be regarded as nonperiodic modulations.’’ Findings from recent studies by Moore and Sek
~Moore and Sek, 1995; Sek and Moore, 1995! strongly support the hypothesis that a place mechanism is used to detect
frequency modulation when the rate of modulation is greater
than about 4 Hz. For a modulation rate of 10 Hz, for example, frequency modulation difference limens ~FMDLs! expressed as a proportion of the equivalent rectangular bandwidth ~ERB! declined slightly with increasing center
frequency between 0.25 and 2 kHz and were essentially constant between 2 and 8 kHz.1 The authors concluded that FMDLs for carrier frequencies below 4 kHz and low modulation
rates ~in the neighborhood of 2 Hz! are determined by a
temporal mechanism, whereas FMDLs for higher modulation
rates are determined by a place mechanism, based on
changes in the excitation pattern, at all carrier frequencies.
0001-4966/96/100(6)/3754/7/$10.00
© 1996 Acoustical Society of America
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3754
Thus some previous studies suggest that changes in frequency are temporally coded ~e.g., Tyler et al., 1983!, some
suggest that they are time or place coded depending on the
rate of change ~Moore and Sek, 1995; Sek and Moore, 1995!
and some are equivocal ~Dooley and Moore, 1988a!. The
present study was designed to extend this area of research by
measuring glide discrimination thresholds over a range of
standard ~i.e., comparison signal! transition sizes, and across
a range of center frequencies. Glide detection thresholds also
were measured. The results then were analyzed to determine
how well they support a place mechanism of glide perception. If frequency change is encoded by such a mechanism,
then an excitation-pattern model should account for the overall pattern of results.
A relatively new procedure was included in the study
that requires some explanation at the outset. The glide discrimination threshold determinations measured the ability to
distinguish between a standard signal that increased in frequency by a fixed amount and a target signal that increased
by a greater amount. If the center frequencies of two such
signals are the same, the subject could simply compare the
end points of the two signals and select the one that is higher
in pitch. If this is the case, the subject is performing a
between-signal pitch comparison which is similar to a DLF
determination, rather than estimating pitch increase from
within-signal information. It is possible that the subjects in
previous glide discrimination studies were making this endpoint comparison. If so, the agreement noted above between
DLFs and glide discrimination thresholds is not surprising.
In the present study, access to between-signal pitch comparisons was denied by roving the center frequencies of the signals, an approach developed by Feth and his colleagues
~Neill and Feth, 1990!. This procedure is described in the
next section. To determine the effect of roving the center
frequencies, the same threshold determinations also were
carried out with nonroved signals.
I. EXPERIMENT 1: GLIDE DIFFERENCE LIMENS FOR
STANDARDS OF FIXED TRANSITION EXTENT
A. Subjects
Four subjects with normal auditory sensitivity participated. All had hearing thresholds of 15 dB HL or less at the
audiometric test frequencies and were paid for their participation.
B. Procedure
In a two-alternative, forced-choice task, the subjects
were asked to identify a target signal which either increased
in frequency ~for the glide detection condition! or increased
more in frequency than the standard signal ~for the glide
discrimination conditions!. The signals were presented
monotically. Thresholds were determined using three standard conditions: ~1! a standard that did not change in frequency ~the 0-Hz standard, in the glide-detection task!, ~2! a
standard that increased by 250 Hz, and ~3! a standard that
increased by 500 Hz. Center frequencies were 0.5, 1, 2, 4,
and 6 kHz, and the end points of the stimuli were linearly
equidistant from their center frequencies. Stimulus duration
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J. Acoust. Soc. Am., Vol. 100, No. 6, December 1996
was 50 ms, with additional rise–fall times of 5 ms. The
intent was to use a signal duration and a range of frequency
transitions that were similar to those of formant transitions,
at least in the lower frequencies.
All center frequency/standard combinations were run in
both a nonroved and a roved condition. In the roved condition, the center frequencies of the signals were randomly
drawn from a uniform distribution with a range equal to 0.1
times the ‘‘nominal’’ center frequency. Thus the actual center frequencies of the 1-kHz signals ranged from 950 to 1050
Hz, the 2-kHz signals from 1900 to 2100 Hz, and so on. The
center frequencies of both the standard and the target were
varied independently both within and between trials. For example, on one trial at the 1-kHz center frequency the subject
might hear a standard with a center frequency of 981 Hz and
a target with a center frequency of 1028 Hz; on the next trial
these values might be 1045 and 1022 Hz, etc. In the nonroved condition, center frequencies did not vary. All signals
were presented at 70 dB SPL, with an interstimulus interval
of 500 ms.
Thresholds were measured using an adaptive procedure
that estimated the 70.7% correct response point on the psychometric function ~Levitt, 1971!. After two consecutive correct responses the change in frequency of the target signal
was decreased; after one incorrect response it was increased.
Step size was decreased after the first six reversals and varied
depending on the center frequency and condition. At center
frequencies of 0.5 and 1 kHz, for the 0-Hz condition, the
initial step size was 10 Hz; at higher center frequencies and
for the 250- and 500-Hz conditions, where thresholds were
greater, initial step sizes ranged up to 40 Hz. Final step sizes
ranged in a similar fashion between 2 and 10 Hz. The frequency increase of the target was not permitted to fall below
that of the standard.
A run consisted of 80 trials, with a break after the first
40. The break was included to maintain alertness, and the
subject was encouraged to remove the headphones, or even
leave the booth, if necessary. The first six reversals were
discarded, giving the subject sufficient opportunity to ‘‘home
in on’’ the threshold area, and threshold was computed as the
arithmetic mean of the subsequent reversals ~always at least
eight!. The subjects were practiced for at least 10 h before
data collection began. For each combination of rove, center
frequency, and standard, they then were tested until performance did not consistently improve over six runs. Of these
six, the runs that varied by more than 1 s.d. from the mean
were discarded, and the threshold calculated from the remaining data ~always at least four runs!. This procedure was
used because for some combinations of conditions considerable within-subject variation was noted. As it turned out,
however, the discarded thresholds were virtually always
those of both the highest and lowest runs, and the resulting
means in fact differed little from the means of all the data in
nearly all cases.
Data collection was completed for each center
frequency-standard-rove combination before the next combination of conditions was begun to facilitate optimal learning
of detection/discrimination cues. The order of standard conditions was counterbalanced within each center frequencyJ. P. Madden and K. M. Fire: Glide discrimination
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3755
TABLE I. Discrimination thresholds expressed as a proportion of equivalent rectangular bandwidth ~ERB! for
the data from experiment 1. Figures in parentheses are standard deviations. ERBs were calculated using the
equation ERB524.7~4.37F11! from Glasberg and Moore ~1990!.
Standard
Frequency
Rove
0 Hz
250 Hz
500 Hz
500
NR
R
0.17 ~0.015!
0.14 ~0.049!
0.25 ~0.073!
0.43 ~0.061!
0.41 ~0.078!
0.46 ~0.210!
1000
NR
R
0.08 ~0.004!
0.10 ~0.020!
0.20 ~0.065!
0.29 ~0.044!
0.29 ~0.047!
0.45 ~0.107!
2000
NR
R
0.07 ~0.019!
0.11 ~0.054!
0.10 ~0.022!
0.17 ~0.016!
0.15 ~0.037!
0.26 ~0.094!
4000
NR
R
0.08 ~0.034!
0.08 ~0.045!
0.07 ~0.026!
0.11 ~0.018!
0.10 ~0.048!
0.21 ~0.025!
6000
NR
R
0.11 ~0.023!
0.13 ~0.033!
0.10 ~0.029!
0.13 ~0.012!
0.12 ~0.029!
0.17 ~0.027!
rove combination, but the order in which the latter
combinations were completed was not randomized or counterbalanced. Performance in the various roved conditions
was rechecked from time to time during data collection,
however, and these thresholds were within the ranges of the
previously obtained thresholds in all cases.
Stimulus presentation and response acquisition were
controlled by a PC. Stimulus and response intervals were
indicated on a computer monitor. The subjects received visual feedback after every trial indicating the stimulus interval
containing the target signal.
changed little with frequency, but glide discrimination
thresholds ~the 250- and 500-Hz standards! increased as frequency decreased at center frequencies below 4 kHz.
To test the statistical significance of the above observations, a three-way analysis of variance ~ANOVA! was performed with rove, standard, and center frequency as factors
and the average thresholds of each subject in each condition
as the dependent variable. The effect of rove was significant
@F~1,119!531.9, p,0.001#, as was the interaction between
rove and standard @F~2,119!, p50.012#. As these results indicated a difference in the effect of standard for the two rove
conditions, the roved and nonroved data were analyzed sepa-
C. Stimulus generation
Digital representations of the stimuli were generated by
an array processor ~TDT-QAP2! running on a PC. A 16-bit
D-to-A converter ~TDT-DD1! operating at a 50-kHz sampling rate converted the digital representations to analog
waveforms which were low-pass filtered at 8 kHz ~TDTFLT3!, attenuated ~TDT-PA3!, and sent through an output
amplifier ~TDT-HBUF3! to an earphone ~Sennheiser HD414SL!. The frequency response of this earphone has been
reported to be relatively smooth over the range of the test
frequencies ~see Moore and Sek, 1995!, and this was confirmed in this laboratory. Signal spectra were verified using
Hypersignal/Workstation spectrum analysis software.
D. Results and discussion
All subjects exhibited the same overall pattern in threshold variation, so only the average thresholds for the various
conditions, expressed as a proportion of the ERB at the corresponding center frequency, are presented in Table I and
Fig. 1. The roved thresholds are higher than the nonroved in
nearly all cases, but the two sets of results display the same
general trends. There was an effect of standard which varied
with center frequency. Thresholds increased as standard transition increased in the lower center frequencies ~0.5 to 2
kHz! but were relatively constant across standard at 4 and 6
kHz. There also was an effect of frequency that varied with
standard. Glide detection thresholds ~the 0-Hz standard!
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J. Acoust. Soc. Am., Vol. 100, No. 6, December 1996
FIG. 1. Average discrimination thresholds for fixed standard transitions expressed as a proportion of the ERB and plotted as a function of center
frequency. Error bars indicate one standard deviation.
J. P. Madden and K. M. Fire: Glide discrimination
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3756
rately. A two-way ANOVA was applied to the nonroved data
with standard and frequency as factors. The main effects of
both standard @F~2,59!519.0, p,0.001# and frequency
@F~4,59!522.1, p,0.001# were significant, as was the interaction @F~8,59!54.2, p,0.001#. Pairwise comparisons were
performed to determine the effect of different levels of standard within the various center frequencies. No significant
differences in threshold were found at the 4- and 6-kHz center frequencies ~p,0.05!. At 2 kHz, the thresholds for the
500-Hz standard were significantly greater than those for the
0-Hz standard. At 1 kHz, the 500- and 250-Hz thresholds
were significantly greater than the 0-Hz thresholds, and at
0.5 kHz, the 500-Hz thresholds were significantly greater
than the 250- and 0-Hz thresholds. Pairwise comparisons
were also performed to determine the effect of different levels of frequency within the three standard conditions. There
were no significant differences in threshold within the 0-Hz
standard. For the 250-Hz standard, thresholds at the 0.5 and
1-kHz center frequencies differed from those at 2, 4, and 6
kHz; the 0.5- and 1-kHz thresholds did not differ from one
another; and the 2-, 4-, and 6-kHz thresholds did not differ
from one another. For the 500-Hz standard, the 0.5- and
1-kHz thresholds differed from all others and the 2-, 4-, and
6-kHz thresholds did not differ from one another.
A two-way ANOVA with standard and frequency as
factors was also applied to the roved thresholds. The results
were similar to those for the nonroved condition. The main
effects of both standard @F~2,59!525.0, p,0.001# and frequency @F~4,59!513.1, p,0.001# were significant, as was
the interaction @F~8,59!53.7, p,0.002#. Pairwise comparisons for the effect of standard within center frequency indicated no significant differences between thresholds within
the 4- and 6-kHz center frequencies. At 0.5 kHz, thresholds
for the 500- and 250-Hz standards differed from the 0-Hz
thresholds; at 1 kHz all conditions differed; at 2 kHz, the
500- and 0-Hz thresholds differed from each other. Pairwise
comparisons for the effect of frequency within standard indicated no significant differences across frequency for the
0-Hz standard. For the 250-Hz standard, thresholds at 0.5
kHz differed from those at 2, 4, and 6 kHz; all other thresholds were the same. For the 500-Hz standard, the 0.5-and
1-kHz thresholds differed from those at 2, 4, and 6 kHz but
not from each other. Overall, the ANOVA results support the
observations made on the basis of Fig. 1 and Table I.
The most striking aspect of the results is the change in
the relationship among the thresholds for the various standard conditions as a function of center frequency. The clear
differences between standards that are present in the low
frequencies decrease as frequency increases and are mainly
absent above 2 kHz. Note that the relationship between standard and number of ERBs traversed also changes with frequency. At 6 kHz all three standards fall within the ERB of
a single auditory filter ~672 Hz!. On the other hand, at 1 kHz
both the 250- and 500-Hz standards span a range greater than
one ERB ~133 Hz!. The data are consistent with the idea that
thresholds are relatively constant as long as the comparison
signal in each standard condition spans less than 1 ERB, but
when the standard span is increased beyond one ERB, the
threshold increases as well. If this is true, glide discrimina3757
J. Acoust. Soc. Am., Vol. 100, No. 6, December 1996
TABLE II. Transition excursions expressed in Hz for the standard signals
used in experiment 2.
Standard
Frequency
500
1000
2000
4000
6000
0.5ERB
1ERB
2ERB
40
67
121
228
336
79
133
241
456
672
158
266
482
912
1344
tion, like glide detection, appears closely linked to auditory
filter bandwidth. Experiment 2 was designed to test this idea.
II. EXPERIMENT 2: GLIDE DIFFERENCE LIMENS FOR
STANDARDS THAT SPAN A CONSTANT
PROPORTION OF ERB
In this experiment, the standard transitions were fixed
proportions of the ERBs at the various center frequencies. It
was hypothesized that discrimination thresholds for transitions of one ERB or less would be roughly equal but that the
threshold would increase significantly for a standard with a
transition significantly greater than one ERB.
A. Conditions
Signal generation and the procedures for threshold estimation were the same as those of experiment 1. The experiment differed only in the magnitude of frequency change for
the standards, which were a fixed proportion of the ERB at
each test frequency. Three standard signals were used: onehalf ERB ~the 0.5ERB standard!, one ERB ~the 1ERB standard!, and two ERB ~the 2ERB standard!. Table II gives the
transition excursions for these standards at the various center
frequencies. Three of the subjects from experiment 1 participated.
B. Results and discussion
The results for experiment 2 are presented in Table III
and Fig. 2. The results from the 0-Hz condition of experiment 1 ~from the three subjects who participated in both
experiments! are included for comparison. The overall pattern was the same across subjects, so only the average
thresholds are presented. The data clearly support the prediction that discrimination thresholds would be relatively constant as long as the frequency transition of the standard signal was within a single ERB, but would increase
significantly when the standard signal spanned a range
greater than a single ERB. Generally, the 2ERB thresholds
are about twice those of the other standard conditions. The
thresholds do not vary greatly across frequency, particularly
in the roved condition, but they are lowest at 1 and 2 kHz.
The data were analyzed statistically to verify these conclusions. As in experiment 1, a three-way ANOVA was performed with rove, standard, and center frequency as factors
and the average thresholds of each subject in each condition
as the dependent variable. The effect of rove again was significant @F~1,119!529.5, p,0.001#, as was the effect of frequency @F~4,119!512.4, p,0.001#. The interaction between
J. P. Madden and K. M. Fire: Glide discrimination
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3757
TABLE III. Discrimination thresholds expressed as a proportion of equivalent rectangular bandwidth for the
data from experiment 2. Figures in parentheses are standard deviations.
Standard
Frequency
Rove
500
NR
R
NR
R
NR
R
NR
R
NR
R
1000
2000
4000
6000
0 Hz
0.15
0.18
0.08
0.10
0.07
0.13
0.10
0.12
0.12
0.16
~0.012!
~0.040!
~0.005!
~0.020!
~0.020!
~0.050!
~0.032!
~0.045!
~0.021!
~0.028!
rove and frequency was nonsignificant @F~4,119!50.8,
p50.491#, as was the interaction between standard and frequency @F~12,119!51.2, p50.281#. The interaction between
rove and standard, while it did not achieve significance at the
0.05 level, was very close to significant @F~3,119!52.4,
p50.071#. Therefore, the effect of standard within the different center frequencies was analyzed separately for the two
rove conditions.
A two-way ANOVA with standard and frequency as
factors was applied to the roved data. The effect of standard
was significant @F~3,59!538.0, p,0.001# as was the effect
of frequency @F~4,59!54.4, p50.005#. The interaction between these two factors was not significant @F~12,59!
50.812#. Pairwise comparisons of the various levels of standard indicated that thresholds for the 2ERB standard differed
0.5ERB
0.09
0.14
0.09
0.10
0.06
0.08
0.09
0.13
0.15
0.16
~0.016!
~0.033!
~0.017!
~0.009!
~0.020!
~0.005!
~0.016!
~0.016!
~0.012!
~0.023!
1ERB
0.12
0.14
0.10
0.10
0.09
0.13
0.12
0.16
0.15
0.18
~0.032!
~0.026!
~0.020!
~0.012!
~0.009!
~0.040!
~0.050!
~0.020!
~0.012!
~0.019!
2ERB
0.25
0.29
0.17
0.24
0.13
0.25
0.21
0.32
0.24
0.28
~0.060!
~0.028!
~0.004!
~0.050!
~0.033!
~0.029!
~0.026!
~0.090!
~0.044!
~0.020!
significantly from all others ~P,0.05! but that differences
among all other standards were nonsignificant. Pairwise
comparisons of the different levels of frequency showed that
the 0.5- and 6-kHz thresholds differed from the 1-kHz
thresholds ~p,0.05!; differences among the other frequencies were not significant.
A two-way ANOVA with standard and frequency as
factors was also applied to the nonroved data. The effect of
standard again was significant @F~3,59!530.4, p,0.001# as
was the effect of frequency @F~4,59!510.4, p,0.001#. The
interaction was not significant @F~12,59!51.1, p50.408#.
Pairwise comparisons of the different levels of standard indicated that the 2ERB thresholds differed from all others
~p,0.05! but that the differences among the other standards
were not significant. Pairwise comparisons of the different
levels of frequency indicated that the 0.5- and 6-kHz thresholds differed from both the 1- and 2-kHz thresholds and that
the 4-kHz threshold differed from the 2-kHz.
In summary, the ANOVA results indicated that ~1! at
each center frequency, the threshold for the 2ERB standard
differs from all others, whereas the thresholds for the 0-Hz,
0.5ERB, and 1ERB standards do not differ; and ~2! there is a
tendency for thresholds at 1 and 2 kHz to be lower than those
at the other center frequencies. These results support the conclusions reached on the basis of Fig. 2.
III. GENERAL DISCUSSION
A. The effect of roving the signals
FIG. 2. As in Fig. 1, but for standard transitions that are a fixed proportion
of the ERB, as indicated in the legend.
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J. Acoust. Soc. Am., Vol. 100, No. 6, December 1996
The interaction between rove and frequency was not significant in either experiment, but the interaction between
rove and standard was significant in the first experiment and
very close to significance in the second. However, in both
experiments separate analyses of the roved and nonroved
data led to essentially the same conclusions. Thus in terms of
threshold variation across center frequency and standard, the
two procedures yielded similar results. If we accept the assumption that roving the signals forced the subjects to use
within-signal cues, the data suggest that mainly within-signal
cues also were used with the nonroved signals.
On the other hand, roving the signals increased the size
of the discrimination thresholds. The overall mean threshold
for the roved signals in the first experiment was 1.3 times
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3758
that of the mean of the roved signals. There are at least two
possible explanations for this. One is that listeners were able
to make at least some use of end-point comparisons between
~as opposed to within! signals in the nonroved condition. If
between-signal end-point comparisons cause the task to resemble a DLF determination, as was suggested in the Introduction, one would expect an increase in threshold at 4 kHz
and especially at 6 kHz. Figure 2 shows a steady increase in
the nonroved thresholds from 2 to 6 kHz that is not as apparent in the roved data. This increase is much smaller than
that found in DLF data ~e.g., Moore, 1973!, however, indicating that the use of the between-signal end-point cue was
of limited utility, possibly because of the short duration of
the signals. An alternative explanation for the smaller nonroved thresholds may be that the standard was repeated
across trials in the nonroved condition. This would have enabled the subjects to sharpen their mental representation of
the standard over the course of a run, thus improving their
performance.
B. Comparison with previous studies
There are no studies in the literature that are directly
comparable to the glide discrimination component of this
study. The most similar study of glide detection is that of
Dooley and Moore ~1988a! mentioned in the Introduction,
which included a level-tone versus up-glide condition. They
obtained thresholds of from 0.7% to 0.9% of center frequency over a frequency range from 0.25 to 8 kHz, with the
lowest thresholds at 1 and 2 kHz. Expressed in Hz, these
thresholds are roughly 0.75 the size of the nonroved thresholds observed in experiment 1, but Dooley and Moore used
500-ms signals in their experiment. They also tested over a
range of durations at 2 kHz, however, and obtained a threshold of around 25 Hz for a 50-ms signal, which is about the
same as the 2-kHz glide detection threshold of experiment 1
in the roved condition. In the present study the lowest average glide detection thresholds also were obtained at 1 and 2
kHz.
In Sek and Moore’s ~1995! study of FM detection, FMDLs expressed as DHz/ERB ranged between 0.04 and 0.055
for the 10-Hz modulation-rate condition. These thresholds
are roughly half those of the present study, but the FM signals would have given the subjects multiple ‘‘looks’’ at the
modulation. For Sek and Moore, FM detection thresholds
were nearly constant, differing by a factor of only 1.4, at
center frequencies between 0.25 and 8 kHz. Thus the glide
detection results of the present study generally are similar to
these previous studies with the exception of the greater magnitudes of the thresholds, which are almost certainly due to
the duration and type of the stimuli.
C. Evaluation of an excitation-pattern model of glide
detection and discrimination
The most commonly used place model of frequency discrimination is that of Zwicker ~1970!, which predicts that the
threshold for detecting a change in frequency should correspond to a fixed change in excitation level on the lowfrequency side of the excitation pattern generated by the
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J. Acoust. Soc. Am., Vol. 100, No. 6, December 1996
FIG. 3. Average discrimination thresholds for the roved signals of experiment 2. The diamond-shaped symbols represent the averages of the four
standard conditions for each center frequency.
stimulus. Zwicker’s model was developed to account for the
detection of frequency modulation, but it possibly can be
extended to account for these glide discrimination results.
Let us assume that in the process of glide discrimination the
listener compares signals by comparing the change in frequency between their respective start and end points. The
accuracy with which this change can be measured would be
determined by the resolution of the location of these points
along the basilar membrane, which in turn would be a function of the steepness of the excitation patterns. Glide discrimination is thus a function of the slope of the excitation
pattern, which in turn is determined by the bandwidth of the
auditory filters centered at and just below the test frequency
~Sek and Moore, 1995!. Therefore, this type of model predicts that the threshold for detection of a change in transition
extent should be a fixed proportion of filter bandwidth.
The results of experiment 2 indicate that when the transition of the comparison signal is either 0 Hz or a constant
proportion of ERB, the discrimination thresholds for the
roved signals in particular approach this prediction. The
thresholds shown in Fig. 2 are replotted as line graphs in Fig.
3 for ease of comparison, along with the average of the
thresholds for all four standard conditions. The 0-Hz and
1ERB conditions display the greatest amount of variation
across frequency, the 2ERB condition the least. The averaged thresholds differ by a factor of 1.4 over the range of
center frequencies. This ratio is very similar to that observed
at the 10-Hz modulation rate by Sek and Moore ~1995!. ~The
Sek and Moore ratio would doubtless have been smaller if
the range of comparison had been limited to that of the
present study; their highest threshold was at 0.25 kHz.! Thus
the results can be said to constitute a ‘‘near miss’’ with respect to the predictions of an excitation pattern model.
J. P. Madden and K. M. Fire: Glide discrimination
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D. Explaining the effect of transition size
ACKNOWLEDGMENTS
The results of experiment 2 also indicated that discrimination thresholds are essentially the same as long as transition size is within one ERB but that discrimination performance begins to worsen at some point ~the precise location
of which cannot be inferred from this experiment! between
transitions of one ERB and two ERBs. In fact, the average of
all thresholds ~roved and nonroved! for the 2ERB standard
~0.238! is almost exactly twice that of the thresholds for
standards that are one ERB or less ~0.120!. This result suggests that the discrimination of glides in frequency follows
Weber’s law, but only when the standard exceeds a certain
transition size. It is of interest that Dooley and Moore
~1988b! found that for glides in level, the Weber fraction for
rate of change discrimination was essentially the same when
standard size was doubled from 5 to 10 dB. This similarity in
the pattern of results for glides in frequency and glides in
level is predicted by an excitation-pattern model, in which
changes in both level and frequency are detected through
changes in level of excitation.
This research was supported by research Grant No. 1
R15 DC 02662-01 from the National Institute on Deafness
and Other Communication Disorders, National Institutes of
Health. We would like to thank Wes Grantham and Brian C.
J. Moore for their helpful comments on earlier versions of
this manuscript.
IV. CONCLUSIONS
For the 50-ms tones used in these experiments:
~1! Glide discrimination results obtained under roved
and nonroved conditions were not statistically equivalent,
but the main conclusions that emerged from the statistical
analyses were the same.
~2! Glide discrimination thresholds expressed as DHz/
ERB varied little across center frequencies ranging from 0.5
to 6 kHz when the frequency transition of the comparison
signal was either 0 Hz or a fixed proportion of the ERB of an
auditory filter at the signal center frequency.
~3! Glide discrimination thresholds were essentially invariant at a given center frequency when the frequency transition of the comparison signal was 0 Hz, 0.5 ERB, or 1
ERB. The average discrimination threshold when the transition of the comparison signal was two ERBs was about twice
the threshold in the other conditions.
~4! The small variation in threshold across center frequency when the transition of the comparison signal is a
fixed proportion of ERB supports an excitation-pattern
model of the discrimination of frequency change. Also, the
pattern of threshold variation as the frequency transition increases suggests that the auditory filters play an important
role in mediating the coding of frequency change.
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J. Acoust. Soc. Am., Vol. 100, No. 6, December 1996
1
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J. P. Madden and K. M. Fire: Glide discrimination
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